# Properties

 Label 30.2.e Level $30$ Weight $2$ Character orbit 30.e Rep. character $\chi_{30}(17,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $4$ Newform subspaces $1$ Sturm bound $12$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$30 = 2 \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 30.e (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(30, [\chi])$$.

Total New Old
Modular forms 20 4 16
Cusp forms 4 4 0
Eisenstein series 16 0 16

## Trace form

 $$4 q - 4 q^{3} - 4 q^{6} - 4 q^{7} + O(q^{10})$$ $$4 q - 4 q^{3} - 4 q^{6} - 4 q^{7} + 4 q^{10} + 4 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{18} + 8 q^{21} - 4 q^{22} - 16 q^{25} - 4 q^{27} - 4 q^{28} - 12 q^{30} - 8 q^{31} - 4 q^{33} - 4 q^{36} + 24 q^{37} + 8 q^{40} + 4 q^{42} + 24 q^{43} - 8 q^{45} + 16 q^{46} + 4 q^{48} - 8 q^{51} + 12 q^{55} - 16 q^{57} - 20 q^{58} - 4 q^{60} - 24 q^{61} - 4 q^{63} + 8 q^{66} - 16 q^{67} + 4 q^{70} - 8 q^{72} - 20 q^{73} + 28 q^{75} + 16 q^{76} + 28 q^{81} - 16 q^{82} + 8 q^{85} + 20 q^{87} - 4 q^{88} + 8 q^{90} + 8 q^{93} + 4 q^{96} + 12 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(30, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
30.2.e.a $4$ $0.240$ $$\Q(\zeta_{8})$$ None $$0$$ $$-4$$ $$0$$ $$-4$$ $$q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$$